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Journal of Environmental Accounting and Management 14(2) (2026) 261--282 | DOI:10.5890/JEAM.2026.06.007

Tharmalingam Gunasekar$^{1}$, Shanmugam Manikandan$^{2,3\dagger}$, Murgan Suba$^{4}$, Ali Akgül$^{3,5,6,7,8\dagger}$,\\ Muhammad Sinan$^{9}$

$^{1}$ Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai, India

$^{2}$ Department of Mathematics, Vel Tech High Tech Dr.Rangarajan Dr.Sakunthala Engineering College, Avadi, Chennai, India

$^{3}$ Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey

$^{4}$ Department of Mathematics, S. A. Engineering College, Chennai, India

$^{5}$ Department of Electronics and Communication Engineering, Saveetha School of Engineering, SIMATS, Chennai, Tamilnadu, India

$^{6}$ Department of Computer Engineering, Biruni University, 34010 Topkapı, Istanbul, Turkey

$^{7}$ Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia /Mersin 10 – Turkey

$^{8}$ Applied Science Research Center. Applied Science Private University, Amman, Jordan

$^{9}$ School of Mathematical Sciences, University of Electronic and Technology of China (UESTC), Sichuan, China 611731

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Abstract

This research develops a deterministic mathematical model for dengue fever transmission using fractal-fractional order differential equations. The proposed model comprises eight compartments, classifying individuals into human and vector populations. By utilizing fixed-point theory, we demonstrate the existence and uniqueness of solutions within the system. We apply fundamental theorems in fractal-fractional calculus alongside the fractional Adams–Bashforth method to obtain approximate solutions. Simulations are performed across various fractional orders and fractal dimensions, offering comparisons with traditional integer-order models. Incorporating fractal-fractional derivatives enhances the model’s ability to capture complex disease dynamics, including memory effects and long-term behavior. This approach provides valuable insights into epidemic control and helps refine intervention strategies. Numerical simulations highlight how arbitrary-order derivatives reveal intricate disease patterns, making them essential for understanding and managing real-world outbreaks.

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